Open Access
August 2019 Cross validation for locally stationary processes
Stefan Richter, Rainer Dahlhaus
Ann. Statist. 47(4): 2145-2173 (August 2019). DOI: 10.1214/18-AOS1743


We propose an adaptive bandwidth selector via cross validation for local M-estimators in locally stationary processes. We prove asymptotic optimality of the procedure under mild conditions on the underlying parameter curves. The results are applicable to a wide range of locally stationary processes such linear and nonlinear processes. A simulation study shows that the method works fairly well also in misspecified situations.


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Stefan Richter. Rainer Dahlhaus. "Cross validation for locally stationary processes." Ann. Statist. 47 (4) 2145 - 2173, August 2019.


Received: 1 May 2017; Revised: 1 February 2018; Published: August 2019
First available in Project Euclid: 22 May 2019

zbMATH: 07082282
MathSciNet: MR3953447
Digital Object Identifier: 10.1214/18-AOS1743

Primary: 62M10
Secondary: 62G20

Keywords: adaptive bandwidth selection , asymptotic optimality , Cross validation , Locally stationary processes

Rights: Copyright © 2019 Institute of Mathematical Statistics

Vol.47 • No. 4 • August 2019
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